Timo Werner was on target for the visitors as the Hammers finished the match with 10-men following Fabian Balbuena's late red card.
The Blues were in cruise control for most of the match and kept the home side on the backfoot, mustering 17 shots, including six on target.
David Moyes' side showed signs of life early on in the second half but couldn't build on it. The 81st minute sending off killed the game off for them.
Despite back-to-back losses, West Ham remain in fifth, a point above Liverpool, while Chelsea strengthened their place in fourth.
Here are the player ratings for Chelsea:
Edouard Mendy - 6/10
With a stoic defense ahead of him, the Chelsea custodian had little to worry about in the match. Whenever he was exposed to West Ham, Mendy came up trumps.
Andreas Christensen - 6.5/10
He almost gifted Jarrod Bowen a chance with an error but recovered well enough to block his effort. Christensen's aerial abilities were there for all to see too.
Thiago Silva - 7/10
Silva deserves credit for keeping the in-form Jesse Lingard quiet in a testament to his control and brilliant man-marking. He kept his cool even when the Hammers appeared threatening as he read the game well and timed his tackles to perfection.
Antonio Rudiger - 7/10
He played a huge role in Chelsea's defense by keeping a weather eye on Bowen and not letting him have much space to work into. Rudiger's use of physical strength to dominate his opposite numbers without getting too aggressive was amazing.
Cesar Azpilicueta - 6/10
The Chelsea skipper operated from an uncharacteristic wing-back position on the right side of the defense and looked hamstrung. He was ineffective going forward and struggled to find spaces to attack from wide areas.
N'Golo Kante - 7/10
He did what he does best, covering every blade of grass and protecting the back four by snuffing out West Ham's attacking moves.
Jorginho - 7/10
Jorginho was at the heart of Chelsea's attack with his intelligent distribution of the ball, but also made sure he didn't leave any space behind him.
Ben Chilwell - 7/10
The former Leicester City full-back provided an outlet and set up Werner for the winner with a brilliant cut back.
Mason Mount - 8/10
He's been one of Chelsea's best players this season and lived up to that reputation with another stormer. Mount was a thorn in West Ham's side, always looking to get in behind their defense, and executed two beautiful long-range efforts.
Timo Werner - 7.5/10
We got to see the Jekyll and Hyde of Werner today. He slotted a confident finish to end his drought and win the match but then missed a sitter that could've fetched him another goal. Still, he'd just be content to have got on the scoresheet in the end.
Christian Pulisic - 6/10
He was involved in the build-up to Werner's goal and tried to find gaps in West Ham's defense, though couldn't provide much spark in the attack.
Hakim Ziyech - 6.5/10
A nice cameo from the Moroccan, who looked bright and got himself involved in the thick of things right after coming on.
Reece James - N/A
James replaced Azpilicueta in the 86th minute but struggled to get involved.
Tammy Abraham - N/A
Another minute later, Abraham was thrown into the mix, but he too could barely do anything.